Measurement of Polystyrene Mean Inner Potential by Transmission Electron Holography of Latex Spheres

Abstract

This study describes the use of transmission electron holography to determine the mean inner potential of polystyrene. Spherical nanoparticles of amorphous polystyrene are studied so that the effect of specimen thickness on the phase shift of an incident electron wave can be separated from the intrinsic refractive properties of the specimen. A recursive four-parameter χ-squared minimization routine is developed to determine the sphere center, radius, and mean inner potential (Φ0) at each pixel in the phase image. Because of the large number of pixels involved, the statistics associated with determining a single Φ0 value characteristic of a given sphere are quite good. Simulated holograms show that the holographic reconstruction procedure and the χ-squared analysis method are robust. Averaging the Φ0 data derived from ten phase images from ten different polystyrene spheres gives a value of Φ0PS = 8.5 V (σ) = 0.7 V). Specimen charging and electron-beam damage, if present, affect the measurement at a level below the current precision of the experiment.

Plasmon resonances and electron phase shifts near Au nanospheres

“…V 0 is a specimendependent quantity, which can be measured using a variety of methods. 2͑a͒, which was fitted to a spherical profile to give an implied mean inner potential of about V 0 = 8.1 V. This value is in accordance with PS sphere off-axis electron holography measurements in the literature, 21 which reported V 0 as 8.5Ϯ 0.7 V. 2͑a͒, which was fitted to a spherical profile to give an implied mean inner potential of about V 0 = 8.1 V. This value is in accordance with PS sphere off-axis electron holography measurements in the literature, 21 which reported V 0 as 8.5Ϯ 0.7 V.…”

Off-axis and inline electron holography: Experimental comparison

“…The charge was modeled as a uniform volume charge with a total charge Q. In order to remove the divergent part of the projected potential and thus make the potential integrable, a charged spherical shell of radius P and total charge Q was added, with P ≫ R. In addition to the total charge of the sphere the following parameters were fitted to the experimental data: R -radius of the sphere (about 92 nm from a simple bright-field TEM image), V 0 -the mean inner potential of the sphere (V 0 of polystyrene is 8.5 V [39]). A fixed dielectric constant of ϵ r = 2.5 [40] has been assumed inside of the sphere.…”

Quantitative TEM-based phase retrieval of MgO nano-cubes using the transport of intensity equation

“…Polyhedra and other simply shaped particles such as spheres [45,46] or cylinders [47,48] have proved useful for benchmarking electron holography experiments [49][50][51], which measure phase shifts more directly than aberrationbased methods. For example, Hibi [52] examined TEM holographic fringe shifts from MgO crystals and asbestos fibres to calculate mean inner potentials and found good agreement, for weakly diffracting orientations, with measurements from other experiments.…”